scholarly journals An Algorithm for Linearizing the Collatz Convergence

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1898
Author(s):  
Alexander Rahn ◽  
Eldar Sultanow ◽  
Max Henkel ◽  
Sourangshu Ghosh ◽  
Idriss J. Aberkane
Keyword(s):  
Dynamical System ◽  
Binary Tree ◽  
Ad Hoc ◽  
Natural Order ◽  
Full Description ◽  
Basin Of Attractions ◽  
The Axiom Of Choice ◽  
Proof Of Convergence ◽  
Computational Properties ◽  
Insight Into

The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers for which the inflation propensity remains so unpredictable it could be used to generate reliable proof-of-work algorithms for the cryptocurrency industry; it has so far resisted every attempt at linearizing its behavior. Here, we establish an ad hoc equivalent of modular arithmetics for Collatz sequences based on five arithmetic rules that we prove apply to the entire Collatz dynamical system and for which the iterations exactly define the full basin of attractions leading to any odd number. We further simulate these rules to gain insight into their quiver geometry and computational properties and observe that they linearize the proof of convergence of the full rows of the binary tree over odd numbers in their natural order, a result which, along with the full description of the basin of any odd number, has never been achieved before. We then provide two theoretical programs to explain why the five rules linearize Collatz convergence, one specifically dependent upon the Axiom of Choice and one on Peano arithmetic.

Designing an Energy Efficient Scheme in MANET using Reconfigurable Directional (RDA) Algorithm

2018 ◽  
Vol 8 (4) ◽  
pp. 92
Author(s):  
Rinkle Chhabra ◽  
Anuradha Saini
Keyword(s):  
Ad Hoc ◽  
Energy Savings ◽  
Setup Time ◽  
Directional Antennas ◽  
Directional Antenna ◽  
Efficient Scheme ◽  
Primary Focus ◽  
Hoc Networks ◽  
Energy Gains ◽  
Insight Into

Mobile Ad Hoc Networks (MANET) are autonomous, infrastructure less and self-configuring networks. MANETs has gained lots of popularity due to on the fly deployment i.e. small network setup time and ability to provide communication in obstreperous terrains. Major challenges in MANETs include routing, energy efficiency, network topology control, security etc. Primary focus in this article is to provide method and algorithm to ensure significant energy savings using re-configurable directional antennas. Significant energy gains can be clinched using directional antenna. Key challenges while using directional antenna are to find destination location, antenna focusing, signal power and distance calculations. Re-configurable directional antenna can ensure significant energy gains if used intelligently. This article provides a brief insight into improved energy savings using re-configurable directional antennas and an associated algorithm

scholarly journals perfectphyloR: An R package for reconstructing perfect phylogenies

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Charith B. Karunarathna ◽  
Jinko Graham
Keyword(s):  
Binary Tree ◽  
Sequence Data ◽  
R Package ◽  
Binary Sequences ◽  
Ancestral Haplotype ◽  
Perfect Phylogeny ◽  
Nested Partitions ◽  
Genetic Sequence ◽  
Insight Into ◽  
Rooted Binary Tree

Abstract Background A perfect phylogeny is a rooted binary tree that recursively partitions sequences. The nested partitions of a perfect phylogeny provide insight into the pattern of ancestry of genetic sequence data. For example, sequences may cluster together in a partition indicating that they arise from a common ancestral haplotype. Results We present an R package to reconstruct the local perfect phylogenies underlying a sample of binary sequences. The package enables users to associate the reconstructed partitions with a user-defined partition. We describe and demonstrate the major functionality of the package. Conclusion The package should be of use to researchers seeking insight into the ancestral structure of their sequence data. The reconstructed partitions have many applications, including the mapping of trait-influencing variants.

scholarly journals Ad Hoc or Institutional Arbitration - A Clear-Cut Distinction? A Closer Look at Borderline Cases

2017 ◽  
Author(s):  
Ulrich G. Schroeter
Keyword(s):  
Ad Hoc ◽  
Theory And Practice ◽  
Present Contribution ◽  
Borderline Cases ◽  
Institutional Rules ◽  
Clear Cut ◽  
Definition Of ◽  
Core Characteristics ◽  
Insight Into ◽  
Mix And Match

It is generally accepted in both theory and practice of arbitration that there are two basic forms of arbitration, ad hoc and institutional. This long established dichotomy has rarely been questioned, and it has mostly worked well in international arbitration practice.The present contribution investigates the traditional distinction between ad hoc and institutional arbitration in more detail by looking at "borderline cases", i.e. constellations that cannot easily be allocated to one of these two categories. Four groups of borderline cases are discussed: (1) UNCITRAL arbitrations, in particular those administered by arbitral institutions; (2) cases in which the parties have chosen institutional rules, but not the issuing institution (and vice versa), (3) the modification of institutional rules by the parties and the identification of a possible "mandatory" core of institutional rules, and (4) "mix and match" (or "hybrid") arbitrations combining one arbitral institution's rules with the case's administration by a different arbitral institution. By identifying the factors that were decisive for these borderline cases being regarded as institutional or ad hoc, the article is trying to gain insight into the core characteristics underlying each arbitration category. Drawing on these insights, it develops and explains a novel definition of "institutional arbitration".

Humility

2018 ◽  
pp. 62-80
Author(s):  
Jeffrey Bilbro
Keyword(s):  
Ad Hoc ◽  
Charles Taylor ◽  
Human Condition ◽  
The Self ◽  
Industrial Economy ◽  
Good Samaritan ◽  
Industrial Culture ◽  
Rational Thought ◽  
Insight Into ◽  
Messy Reality

When faced with moral or environmental problems, the industrial culture searches for a set of rules that can guide us through a messy reality. Yet these codes arrogantly foreclose a complex reality and provide a false assurance of propriety; as such, they are ways of keeping the self buffered. Berry, following thinkers such as Ivan Illich and Charles Taylor, turns to the parable of the Good Samaritan for insight into the embodied, humble forms of love that would characterize a truly sustainable community. His essays practice such humility not by being deferential or meek, but by recognizing that the human condition requires us to choose and act from a position of irremediable ignorance. Worse still, we humans generally don’t act on the basis of our most careful, rational thought, but on a more gut level. The occasional, ad hoc nature of his essays evinces his efforts to walk along what he terms a “way of ignorance,” a way of approaching reality in light of our condition as finite persons. In addition, many of Berry’s essays are structured by binaries—boomers versus stickers, the industrial economy versus the Kingdom of God—that work to pry open the codes we use to foreclose reality.

scholarly journals A backward analysis for constraint logic programs

2002 ◽  
Vol 2 (4-5) ◽  
pp. 517-547 ◽  
Author(s):  
ANDY KING ◽  
LUNJIN LU
Keyword(s):  
Ad Hoc ◽  
Abstract Interpretation ◽  
Logic Program ◽  
Control Flow ◽  
Third Party ◽  
Logic Programs ◽  
Abstract Domains ◽  
Constraint Logic Programs ◽  
Backward Analysis ◽  
Computational Properties

One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If the logic program does not come with any documentation, then the programmer is forced to either experiment with queries in an ad hoc fashion or trace the control-flow of the program (backward) to infer the modes in which a predicate must be called so as to avoid an instantiation error. This paper presents an abstract interpretation scheme that automates the latter technique. The analysis presented in this paper can infer moding properties which if satisfied by the initial query, come with the guarantee that the program and query can never generate any moding or instantiation errors. Other applications of the analysis are discussed. The paper explains how abstract domains with certain computational properties (they condense) can be used to trace control-flow backward (right-to-left) to infer useful properties of initial queries. A correctness argument is presented and an implementation is reported.

scholarly journals An Improved Bytewise Approximate Matching Algorithm Suitable for Files of Dissimilar Sizes

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 503
Author(s):  
Víctor Gayoso Martínez ◽  
Fernando Hernández-Álvarez ◽  
Luis Hernández Encinas
Keyword(s):  
Digital Forensics ◽  
Ad Hoc ◽  
Full Description ◽  
Matching Algorithm ◽  
Approximate Matching ◽  
Digital Devices ◽  
Signature Generation ◽  
Actual Content ◽  
Similarity Preserving ◽  
Generation Procedure

The goal of digital forensics is to recover and investigate pieces of data found on digital devices, analysing in the process their relationship with other fragments of data from the same device or from different ones. Approximate matching functions, also called similarity preserving or fuzzy hashing functions, try to achieve that goal by comparing files and determining their resemblance. In this regard, ssdeep, sdhash, and LZJD are nowadays some of the best-known functions dealing with this problem. However, even though those applications are useful and trustworthy, they also have important limitations (mainly, the inability to compare files of very different sizes in the case of ssdeep and LZJD, the excessive size of sdhash and LZJD signatures, and the occasional scarce relationship between the comparison score obtained and the actual content of the files when using the three applications). In this article, we propose a new signature generation procedure and an algorithm for comparing two files through their digital signatures. Although our design is based on ssdeep, it improves some of its limitations and satisfies the requirements that approximate matching applications should fulfil. Through a set of ad-hoc and standard tests based on the FRASH framework, it is possible to state that the proposed algorithm presents remarkable overall detection strengths and is suitable for comparing files of very different sizes. A full description of the multi-thread implementation of the algorithm is included, along with all the tests employed for comparing this proposal with ssdeep, sdhash, and LZJD.

Maasai Age-Sets and Prophetic Leadership: 1850–1910

Africa ◽  
1979 ◽  
Vol 49 (2) ◽  
pp. 134-146 ◽  
Author(s):  
John L. Berntsen
Keyword(s):  
Ad Hoc ◽  
Professional Services ◽  
Colonial Power ◽  
East African ◽  
The People ◽  
History Of ◽  
Initial Interaction ◽  
Opening Paragraph ◽  
The Relationship ◽  
Insight Into

Opening ParagraphIn their initial interaction with the Colonial powers, several East African peoples such as the Maasai, the Turkana, the Sebei, the Karamojong, and the Nandi—all organized through some type of age-based institution—united around prophetic leaders, diviners, or ritual experts who mobilized men from several territorial sections to confront the intruders. This ad hoc military unity was necessarily short-lived, usually ending with the defeat of the people by the colonial power and see the imprisonment or death of the prophetic leader involved. (See Fosbrooke 1948: 12-19; Merker 1910: 67-105; Jacobs 1965: 20-108; Dyson-Hudson 1966: 15-16; Gulliver 1950: 229, 240; Meinertzhagen 1956: 222 ff; Weatherby 1962: 200-12; 1967: 133-44; Lamphear 1976: 225-43.) While ethnological studies of various age-organizations often mention that diviners or prophets provided professional services for the members of an age-group at their ceremonies, no one has examined the process by which a prophetic leader or diviner established his legitimacy during periods of peace so that he might lead the people during times of crisis. An examination of the prophetic institution among the Maasai and the relationship between the prophets and the members of the age-sets may provide some insight into the process, especially the manner in which prophets emerged as leaders of the people during two major crises in the history of the Purko-Kisongo Maasai: the Ilaikipiak war and the rinderpest pan-zootic.

Unravelling Nature's networks

2003 ◽  
Vol 31 (6) ◽  
pp. 1457-1461 ◽  
Author(s):  
N.A.M. Monk
Keyword(s):  
Dynamical System ◽  
Mathematical Modelling ◽  
Computational Analysis ◽  
Spatiotemporal Dynamics ◽  
Interaction Networks ◽  
Living Systems ◽  
Cellular Interaction ◽  
Cellular Mechanisms ◽  
Complex Dynamical System ◽  
Insight Into

Dramatic progress has been made recently in determining the genetic and molecular composition of cells. This has prompted the development of new approaches to the challenge of understanding how basic cellular mechanisms are coordinated to produce the dazzling complexity of living systems. To face this challenge fully, it is critical not only to know what genes and proteins are expressed in cells, but also to understand the spatiotemporal dynamics of their networks of interactions. The sheer scale and complexity of cellular interaction networks necessitates a multi-disciplinary effort in which sophisticated experimental techniques are employed in combination with computational analysis and mathematical modelling. Such approaches are beginning to provide insight into basic structures and mechanisms, and promise to become critical to the post-genomic mission of understanding the cell as a complex dynamical system.

Workplace Satisfaction Before and After Move to an Open Plan Office - Including Interactions with Gender and Introversion

2017 ◽  
Vol 61 (1) ◽  
pp. 455-459 ◽  
Author(s):  
Nathan Bos ◽  
Kylie Molinaro ◽  
Alexander Perrone ◽  
Kelly Sharer ◽  
Ariel Greenberg
Keyword(s):  
Ad Hoc ◽  
Additional Data ◽  
Small Sample Size ◽  
Small Sample ◽  
Workplace Satisfaction ◽  
Flexible Support ◽  
Before And After ◽  
Open Plan ◽  
Data Source ◽  
Insight Into

Open plan offices are both popular and controversial. We studied the response of a group moving from shared, but closed offices to an open plan office. The main data source reported here is a workplace satisfaction survey given pre-move, post-move, and to a lab baseline comparison group at the same organization, with some additional data from observations and interviews. Workers moving to the open plan office appreciated the flexible support for collaboration and the space’s appearance. There was lower satisfaction related to space for private concentrated work, temperature control, and ability to have private conversations. There were also some statistical interactions suggesting more positive responses by males and less positive responses by introverts; analysis was limited by small sample size. Observations and interviews gave further insight into open plan “neighborhoods” and the design of ad hoc spaces.

Dynamics of quark-bag vibrations: validity of the adiabatic approximation

1984 ◽  
Vol 62 (3) ◽  
pp. 260-270 ◽  
Author(s):  
Y. Nogami ◽  
Lauro Tomio
Keyword(s):  
Surface Tension ◽  
Ad Hoc ◽  
Adiabatic Approximation ◽  
Inertial Mass ◽  
Roper Resonance ◽  
First Excited State ◽  
Quark Level ◽  
Quark System ◽  
The Masses ◽  
Insight Into

In order to gain an insight into the nature of possible quark–bag vibrations, we consider a schematic "dynamical bag model" for hadrons. The model consists of a spherical bag with an ad hoc inertial mass and surface tension, and the quarks it contains. The bag and quarks are both treated nonrelativistically, and the Schrödinger equation for the coupled bag–quark system is solved. It is found that the adiabatic approximation, which is meant for a bag much heavier than the quark, describes the first excited state of the bag vibration quite well even if the masses of the bag and quark are comparable. This bag excitation simulates the Roper resonance in the nucleon sector. For a bag level which is nearly degenerate with a quark level (of the same parity, etc.) in the adiabatic approximation, the approximation naturally fails.

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